How many integers are divisible by at least one of the numbers $4$,$ 7$ and $33$?

Question

Find how many integers $N$ satisfying $1≤n≤5000$ are divisible by at least one of the numbers $4$, $7$ and $33$ ?

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I did solve this by using Inclusion - Exclusion and got correct but by using Euler's Totient Function, I not not able to get correct one.

Such numbers will be total 5000 - $φ(5000)$.

Hence, $φ(5000)$ = $2^3.5^4$ = $2000$

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Well, Where am I wrong here ?

Answer 1

The totient function you've computed is correct, but completely unrelated to the problem at hand.

$\phi(5000)$ answers the question: how many numbers $n\leq 5000$ are relatively prime to $5000$? It has nothing to do with the 4, 7, or 33 stated in your question.